The broad, long-term objectives of this research are to elucidate the fundamental principles and mechanisms of hydrogen transfer in both protein and RNA enzyme catalysis. These objectives will be accomplished with a broad range of theoretical and computational methods, including quantum mechanical/molecular mechanical calculations, classical molecular dynamics simulations, and hybrid quantum/classical molecular dynamics simulations that provide atomic-level information about structural rearrangements and conformational motions during the catalyzed chemical reaction. These calculations will probe the roles of hydrogen bonding, electrostatics, active site reorganization, and conformational sampling in both protein and RNA enzyme catalysis. These theoretical studies will be performed in close collaboration with experimental groups, assisting in the interpretation of experimental data and providing experimentally testable predictions. The first two specific aims center on the enzyme ketosteroid isomerase (KSI), which catalyzes the isomerization of steroids. The first specific aim is to probe the role of hydrogen bonding in KSI, focusing on inductive effects along the hydrogen-bonding network, coupling among the hydrogen bonds, and the role of water molecules in the active site. The second specific aim is to examine the significance of enzyme motion in KSI, focusing on active site reorganization, conformational sampling, and the impact of distal mutations. These two specific aims will provide predictions related to several different types of experimental data, including NMR chemical shifts and electronic absorption spectra of inhibitors, time-dependent Stokes shifts of bound photoacids, and kinetics of mutants. This strong connection between theory and experiment provides an opportunity to dissect fundamental issues pertaining to hydrogen transfer reactions in enzymes. The last two specific aims center on the hepatitis delta virus (HDV) RNA enzyme (ribozyme), which catalyzes the cleavage of an internal phosphodiester bond. These two specific aims are motivated by the recent solution of a catalytically competent pre-cleaved crystal structure of this ribozyme. The third specific aim is to elucidate the proton transfer mechanism in the HDV ribozyme, focusing on the catalytic roles of a cytosine nucleotide and a magnesium ion in the active site. The fourth specific aim is to understand the role of motion in the HDV ribozyme, focusing on the correlated motions and the conformational changes occurring during the catalyzed chemical reaction. The biomedical relevance of this ribozyme is that HDV increases the severity of liver diseases caused by hepatitis B virus, and replication of HDV depends on self-cleavage of the HDV ribozyme. All of these studies are relevant to public health because the elucidation of the underlying fundamental principles of enzyme catalysis will facilitate the design of more efficient enzymes and inhibitors, thereby potentially assisting in the development of more effective drugs for a wide range of diseases. Furthermore, insights into RNA catalysis may assist in the development of ribozymes for use as therapeutic agents to cleave pathogenic RNAs.